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3 angle bicectors concur with OI

Source: Sharygin Finals 2022 10.6

October 26, 2022
geometryconcurrencyconcurrent

Problem Statement

Let O,IO, I be the circumcenter and the incenter of triangle ABCABC, PP be an arbitrary point on segment OIOI, PAP_A, PBP_B, and PCP_C be the second common points of lines PAPA, PBPB, and PCPC with the circumcircle of triangle ABCABC. Prove that the bisectors of angles BPACBP_AC, CPBACP_BA, and APCBAP_CB concur at a point lying on OIOI.
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